Quantum fluctuations of lightcone in 4-dimensional spacetime with parallel plane boundaries

TL;DR

This paper investigates how quantum fluctuations of the lightcone in a 4D spacetime are affected by boundary conditions and confinement between two parallel planes, revealing that Neumann conditions and multiple boundaries amplify these fluctuations.

Contribution

It demonstrates that boundary conditions and the presence of multiple parallel planes significantly influence quantum lightcone fluctuations in 4D spacetime.

Findings

Neumann boundary conditions lead to greater fluctuations than Dirichlet.

Quantum fluctuations are larger with two planes than with a single plane.

Confinement of gravitons enhances quantum fluctuations due to the uncertainty principle.

Abstract

Quantum fluctuations of lightcone are examined in a 4-dimensional spacetime with two parallel planes. Both the Dirichlet and the Neumann boundary conditions are considered. In all the cases we have studied, quantum lightcone fluctuations are greater where the Neumann boundary conditions are imposed, suggesting that quantum lightcone fluctuations depend not only on the geometry and topology of the spacetime as has been argued elsewhere but also on boundary conditions. Our results also show that quantum lightcone fluctuations are larger here than that in the case of a single plane. Therefore, the confinement of gravitons in a smaller region by the presence of a second plane reinforces the quantum fluctuations and this can be understood as a consequence of the uncertainty principle.